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International Conference on Geometric Science of Information

GSI 2015: Geometric Science of Information pp 558–565Cite as

Enlargement, Geodesics, and Collectives

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Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 9389))

Abstract

We investigate optimal control of systems of particles on matrix Lie groups coupled through graphs of interaction, and characterize the limit of strong coupling. Following Brockett, we use an enlargement approach to obtain a convenient form of the optimal controls. In the setting of drift-free particle dynamics, the coupling terms in the cost functionals lead to a novel class of problems in subriemannian geometry of product Lie groups.

This research was supported in part by the Air Force Office of Scientific Research under AFOSR Grant No. FA9550-10-1-0250, the ARL/ARO MURI Program Grant No. W911NF-13-1-0390, and by the Office of Naval Research.

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References

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Acknowledgment

It is a pleasure to acknowledge stimulating discussions with Roger Brockett on the subject of this paper

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, Institute for Systems Research, University of Maryland, College Park, 20742, USA

    P. S. Krishnaprasad

  2. Naval Research Laboratory, Washington, DC, 20375, USA

    Eric W. Justh

Authors
  1. Eric W. Justh
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  2. P. S. Krishnaprasad
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Corresponding author

Correspondence to P. S. Krishnaprasad .

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Editors and Affiliations

  1. Bâtiment Alan Turing, CS35003, École Polytechnique, Palaiseau, France

    Frank Nielsen

  2. Thales Land\& Air Systems, Limours, France

    Frédéric Barbaresco

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Justh, E.W., Krishnaprasad, P.S. (2015). Enlargement, Geodesics, and Collectives. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2015. Lecture Notes in Computer Science(), vol 9389. Springer, Cham. https://doi.org/10.1007/978-3-319-25040-3_60

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  • DOI: https://doi.org/10.1007/978-3-319-25040-3_60

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-25039-7

  • Online ISBN: 978-3-319-25040-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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